Invasion threshold in structured populations with recurrent mobility patterns.

Area of Science:

• Epidemiology
• Network Science
• Mathematical Biology

Background:

• Contagion and spreading processes are complex in structured populations.
• Understanding disease dynamics in metapopulations requires accounting for individual movement and memory.
• Existing models often simplify mobility or lack memory effects.

Purpose of the Study:

• To develop a framework for analyzing contagion in complex subpopulation networks with individual memory.
• To incorporate memory of origin into metapopulation epidemic models.
• To derive an explicit global epidemic invasion threshold.

Main Methods:

• Developed a metapopulation model with heterogeneous fluxes and memory of residence.
• Integrated the susceptible-infectious-recovered (SIR) model within subpopulations.
• Utilized degree-block variables and time-scale separation for analytical insight.
• Considered the stochastic nature of the epidemic process.

Main Results:

• Obtained an explicit expression for the global epidemic invasion threshold.
• This threshold prevents widespread disease below a critical value.
• The threshold depends on disease parameters, mobility rates, and network coupling.

Conclusions:

• The framework provides insight into mechanisms controlling disease spread in structured communities.
• The derived threshold is absent in continuous deterministic models and highlights the importance of memory and mobility.
• This work advances the understanding of contagion dynamics in spatially structured populations.